Great question! Unfortunately I'm not really sure.
In languages like German and Danish, etc, the indefinite article is implied when you're talking about a person and their profession: «Han er dommer. Min mor er advokat. Pigen er ingeniør.» However, every sentence I've seen that applies an attribute to a person includes the indefinite article: «Hun er en dreng. Det er en farverig fugl. En bamse er en legetøj.»
That being said, translation's not an exact science, but more of an art, and to most speakers of American English it's acceptable to say "He is a vegetarian," so I'd say that if it makes sense in your head to translate it that way, then translate it that way.
Are there any native speakers that can chime in?
It is no less correct to say "The man is a vegetarian", but it adds an extra article when it could just be "The man is vegetarian." To my knowledge, adding an extra article will not change the meaning of a sentence; it is more of a "filler word," I would think.
Edit: on second thought, I would think that adding the extra article, while not contributing to the meaning, may confuse someone. It might indicate that the following word is an adjective and when it is not, then it is like "zOiNK, yoU wErE FoOlEd." By that, I mean it may confuse someone by making them think something is coming after the word "Vegetarian"
(ex. The man is a vegetarian sympathizer; The man is a vegetarian dietitian; etc;)